Consistent and efficient reconstruction of latent tree models

Abstract

We study the problem of learning a latent tree graphical model where samples are available only from a subset of variables. We propose two consistent and computationally efficient algorithms for learning minimal latent trees, that is, trees without any redundant hidden nodes. Our first algorithm, recursive grouping, builds the latent tree recursively by identifying sibling groups. Our second and main algorithm, CLGrouping, starts with a pre-processing procedure in which a tree over the observed variables is constructed. This global step guides subsequent recursive grouping (or other latent-tree learning procedures) on much smaller subsets of variables. This results in more accurate and efficient learning of latent trees. We compare the proposed algorithms to other methods by performing extensive numerical experiments on various latent tree graphical models such as hidden Markov models and star graphs.